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Popular >

derivative of (2x+6)/(x+9)

Solution

derivative of

\frac{2 x + 6}{x + 9}

Solution

\frac{12}{( x + 9 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{2 x + 6}{x + 9})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( 2 x + 6 ) ( x + 9 ) - \frac{d}{d x} ( x + 9 ) ( 2 x + 6 )}{( x + 9 ) ^{2}}

\frac{d}{d x} (2 x + 6) = 2

\frac{d}{d x} (x + 9) = 1

= \frac{2 ( x + 9 ) - 1 \cdot ( 2 x + 6 )}{( x + 9 ) ^{2}}

Simplify

\frac{2 ( x + 9 ) - 1 \cdot ( 2 x + 6 )}{( x + 9 ) ^{2}} : \frac{12}{( x + 9 ) ^{2}}

= \frac{12}{( x + 9 ) ^{2}}

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Frequently Asked Questions (FAQ)

What is the derivative of (2x+6)/(x+9) ?
The derivative of (2x+6)/(x+9) is (12)/((x+9)^2)
What is the first derivative of (2x+6)/(x+9) ?
The first derivative of (2x+6)/(x+9) is (12)/((x+9)^2)